Given n bins, and toss balls, each toss the ball is equally like to end up in any bin. If a bin get a ball, move this bin away so that following tosses will not fall in this bin again, what's the expected number of ball tosses to get a ball in a specific bin.
2026-03-27 18:09:28.1774634968
The expected number of ball tosses to get a ball in a specific bin.
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Hint for alternate approach: Say you have $n$ balls as well, and they are numbered. And you throw all of them in order, regardless of whether you already hit the specified bin. Then each bin has a numbered ball in it, and the number of throws it took to hit the specific bin is exactly equal to the number on the ball in it. What is the expected number on that ball?